Communications in Mathematical Physics

, Volume 370, Issue 3, pp 895–923 | Cite as

Spectral Flow of Monopole Insertion in Topological Insulators

  • Alan L. Carey
  • Hermann Schulz-BaldesEmail author


Inserting a magnetic flux into a two-dimensional one-particle Hamiltonian leads to a spectral flow through a given gap which is equal to the Chern number of the associated Fermi projection. This paper establishes a generalization to higher even dimension by inserting non-abelian monopoles of the Wu-Yang type. The associated spectral flow is then equal to a higher Chern number. For the study of odd spacial dimensions, a new so-called ‘chirality flow’ is introduced which, for the insertion of a monopole, is then linked to higher winding numbers. This latter fact follows from a new index theorem for the spectral flow between two unitaries which are conjugates of each other by a self-adjoint unitary.


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We thank the referees and Nora Doll for several constructive comments on the first draft of this paper. The work of A. L. C. was supported by the Australian Research Council, that of H. S.-B. partially by the DFG.


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Authors and Affiliations

  1. 1.Mathematical Sciences InstituteAustralian National UniversityCanberraAustralia
  2. 2.School of Mathematics and Applied StatisticsUniversity of WollongongWollongongAustralia
  3. 3.Department MathematikFriedrich-Alexander-Universität Erlangen-NürnbergErlangenGermany

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